A solid has a structure in which `W` atoms are located at the corners of a cubic lattice, `O` atom at the centre of edges, and `Na` atom at the centre of the cube. The formula for the compound is

Options

A. `NaWO_(2)`
B. `NaWO_(3)`
C. `Na_(2)WO_(3)`
D. `NaWO_(4)`

Explanation

To determine the formula for the compound based on the given structure, we need to analyze the contributions of each type of atom in the unit cell.

### Step 1: Identify the positions of the atoms
- **W (Tungsten) atoms** are located at the corners of the cubic lattice.
- **O (Oxygen) atoms** are located at the center of the edges.
- **Na (Sodium) atom** is located at the center of the cube.

### Step 2: Calculate the contribution of W atoms
- There are 8 corners in a cube, and each corner atom contributes \( \frac{1}{8} \) of its atom to the unit cell.
- Therefore, the total contribution from W atoms is:
\[ \text{Total W atoms} = 8 \times \frac{1}{8} = 1 \]

### Step 3: Calculate the contribution of O atoms
- There are 12 edges in a cube, and each edge atom contributes \( \frac{1}{4} \) of its atom to the unit cell.
- Therefore, the total contribution from O atoms is:
\[ \text{Total O atoms} = 12 \times \frac{1}{4} = 3 \]

### Step 4: Calculate the contribution of Na atoms
- The Na atom is located at the center of the cube, which means it contributes fully to the unit cell.
- Therefore, the total contribution from Na atoms is:
\[ \text{Total Na atoms} = 1 \]

### Step 5: Combine the contributions to write the formula
- Now we combine the contributions of each type of atom:
- W: 1
- O: 3
- Na: 1
- Thus, the formula for the compound is:
\[ \text{Formula} = \text{Na} \text{W} \text{O}_3 \]

### Final Answer
The formula for the compound is **NaWO₃**.

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